The video uses humor to tell Carroll's story, with actresses portraying the ineffectual airline customer service reps, Carroll's bandmates singing backup while wearing sombreros and fake black mustaches, and guitars flying through the air.
The song's refrain goes: "United, you broke my Taylor guitar/United, some big help you are/You broke it/ You should fix it/ You're liable, just admit it/I should have flown by someone else or gone by car/Because United breaks guitars."
Carroll said he didn't write the songs to get even with the airline -- or even get compensation.
"I'm not out to harm the company," he said. "My initiative was to feel good about writing the songs."
But he is happy with the company's apology.
"This could end up being a very positive thing for passengers on United and across the industry," he said.